## Positive Nested Conceptual Graphs (0)

Venue: | Proc. 5th Int’l Conf. on Conceptual Structures (ICCS 97), Springer Verlag, LNAI 1257 |

Citations: | 16 - 2 self |

### BibTeX

@INPROCEEDINGS{Chein_positivenested,

author = {Michel Chein and Marie-laure Mugnier},

title = {Positive Nested Conceptual Graphs},

booktitle = {Proc. 5th Int’l Conf. on Conceptual Structures (ICCS 97), Springer Verlag, LNAI 1257},

year = {},

pages = {95--109},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

. This paper deals with positive (i.e. without negation) nested conceptual graphs (NCGs). We first give a general framework - graphs of graphs provided with morphism - for defining classes of NCGs. Then we define a new class of NCGs - typed NCGs - and we show that known kinds of NCGs can be described very simply as classes of the general framework. All NCG models considered generalize the simple CG model in the sense that they involve objects which are generalizations of simple CGs and reasonings on these objects are based on a graph operation (projection) which is a generalization of that used for simple CGs. Furthermore, the general framework introduced allows one to consider all these models as slight variations of a unique notion. This study has been initiated by applications we are currently involved in. 1. Introduction The work reported in this paper concerns conceptual graphs (CGs) for representing and reasoning on hierarchically structured knowledge. In these CGs, ...

### Citations

10922 |
Computers and Intractability: A Guide to the Theory of NP-Completeness
- Garey, Johnson
- 1979
(Show Context)
Citation Context ...Gs provided with projection (see part 3) are categories. In order to compare two models of nested CGs, or more generally two categories, we use the problem reduction notion of complexity theory (e.g. =-=[15]-=-). The following definition is obtained by considering the problem of the existence of a morphism between two objects, which is also the problem of subsumption checking. Definition 5. Let C and D be t... |

348 | Notes on formalizing context
- McCarthy
- 1993
(Show Context)
Citation Context ...he transformation from a 2-NCG to an untyped NCG is trivial. On the other hand, for typed NCGs a new study seems to be more appropriate. There are possible links between NCGs and contextual reasoning =-=[21]-=-, although contextual reasoning is not our goal here. But both logical semantics mentioned above do not seem to be close to one of the logical formalizations of contextual reasoning (e.g. [22], [23]).... |

191 |
Contexts: A Formalization and Some Applications
- Guha
- 1991
(Show Context)
Citation Context ...asoning [21], although contextual reasoning is not our goal here. But both logical semantics mentioned above do not seem to be close to one of the logical formalizations of contextual reasoning (e.g. =-=[22]-=-, [23]). However, a more in-depth comparison has to be done. Acknowledgments We would like to thank G. Kerdiles and E. Salvat for their comments on a previous version of this paper, and specially G. s... |

101 | Quantificational Logic of Context
- Buvač
- 1996
(Show Context)
Citation Context ...g [21], although contextual reasoning is not our goal here. But both logical semantics mentioned above do not seem to be close to one of the logical formalizations of contextual reasoning (e.g. [22], =-=[23]-=-). However, a more in-depth comparison has to be done. Acknowledgments We would like to thank G. Kerdiles and E. Salvat for their comments on a previous version of this paper, and specially G. simonet... |

55 |
Conceptual graphs: fundamental notions. Revue dé Intelligence Artificielle
- Chein, Mugnier
- 1992
(Show Context)
Citation Context ...CGs introduced in [2], chap. 3). The fundamental operation for reasonings is projection, which is a morphism between these objects. Since it is sound [2] and complete (when graphs have a normal form, =-=[3]-=-) with respect to deduction in first order logic, reasonings on simple CGs can be based on projection computing. Furthermore, projection induces a structural subsumption relation on simple CGs. All NC... |

17 |
Représenter des connaissances et raisonner avec des graphes », Revue d'intelligence artificielle
- Mugnier, Chein
- 1996
(Show Context)
Citation Context ...mework for formalizing and comparing NCG classes provided with a subsumption relation. In what follows, we give three examples of NCG classes. 3.1. Untyped NCGs A class of NCGs has been introduced in =-=[18]-=-. In order to distinguish this class from the others, we call it untyped NCG in this paper. Labels of concept nodes are triples (t, m, d). t and m respectively represent the type and the referent of t... |

14 |
Conceptual Graphs as a Universal Knowledge Representation
- Sowa
- 1992
(Show Context)
Citation Context ...l levels and reasoning must respect these levels. A convenient way of encoding these levels is to put simple CGs within simple CGs. Descending from level to level can be seen as a "zooming" =-=operation [9]-=-[10]. This led us to a first NCG model. In these NCGs, concept nodes are labelled with three fields: to the type and referent is added a description, which may be either generic (i.e. empty) or a set ... |

10 |
Logical foundations for representing object-oriented systems
- Sowa
- 1993
(Show Context)
Citation Context ...evels and reasoning must respect these levels. A convenient way of encoding these levels is to put simple CGs within simple CGs. Descending from level to level can be seen as a "zooming" ope=-=ration [9][10]-=-. This led us to a first NCG model. In these NCGs, concept nodes are labelled with three fields: to the type and referent is added a description, which may be either generic (i.e. empty) or a set of N... |

7 |
A Logic for Nested Graphs
- Preller, Mugnier, et al.
- 1998
(Show Context)
Citation Context ...he corollary question is whether projection is sound and complete with respect to this semantics. This point has been studied for untyped NCGs provided with coreference links, with two approaches. In =-=[19] a "n-=-on-classical" logic is defined, with a sequent calculus working on these formulas. Projection is proven to be sound and complete with respect to this calculus, i.e. there exists a projection from... |

4 |
Modelling and simulating human behaviours with conceptual graphs
- Bos, Botella, et al.
- 1997
(Show Context)
Citation Context ...owledge involved. Let us give two examples of applications we are currently involved in. First, a simulation application of the required behavior of human agents in case of a catastrophe in a factory =-=[6]-=- [7]. This behavior is described by CGs which represent situations, pre-conditions and postconditions of actions to be performed, each of these elements being themselves described by CGs. Second, a st... |

3 |
Semantic Networks are in the eye of the Beholder
- Schubert
- 1991
(Show Context)
Citation Context ...r the sake of brevity, we simply call them nested CGs (NCGs). Let us first recall that we develop the CG model as a graphical knowledge representation model, where "graphical" is used in the=-= sense of [1], that is -=-a model that "uses graph-theoretic notions in an essential and nontrivial way". Basic objects are simple CGs (SCGs), which are connected labelled bipartite graphs (they correspond to the CGs... |

3 |
Using Contexts to Represent Text
- Dick
- 1994
(Show Context)
Citation Context ...somorphism between categories. 3. Nested Conceptual Graphs All kinds of (positive) nested CGs we found in papers can be defined as trees of C-graphs where C is a class of simple CGs (e.g. [10], [16], =-=[17]-=-, [12]; more generally, see ICCS proceedings). This is not surprising since trees precisely are the underlying structure of boxes within boxes. As the case may be, trees of SCGs may have labelled edge... |

2 |
La plate-forme CoGITo : manuel d'utilisation
- Haemmerl
- 1995
(Show Context)
Citation Context ...ctural subsumption relation on simple CGs. All NCG models considered in this paper generalize this simple CG model, while preserving its properties. The simple CG model has been implemented on CoGITo =-=[4]-=- [5], a software platform for developing knowledge-based applications for which every piece of knowledge is represented by CGs. But in several applications this model proved to be inconvenient for exp... |

2 |
Computational Situation Theory in the Conceptual Graph Language
- Ghosh, Wuwongse
- 1996
(Show Context)
Citation Context ... referent is added a description, which may be either generic (i.e. empty) or a set of NCGs. Projection is recursively defined according to the recursive structure of NCGs. Let us specify that in [11]=-=[12]-=- a model close to NCGs is defined (but projection in this latter model is not recursive). It appeared in applications that a mean of specifying the semantics of nestings was desirable. This led us to ... |

2 |
Representing natural language causality in conceptual graphs: the higher order conceptual relation problem
- Nazarenko
- 1993
(Show Context)
Citation Context ...n of isomorphism between categories. 3. Nested Conceptual Graphs All kinds of (positive) nested CGs we found in papers can be defined as trees of C-graphs where C is a class of simple CGs (e.g. [10], =-=[16]-=-, [17], [12]; more generally, see ICCS proceedings). This is not surprising since trees precisely are the underlying structure of boxes within boxes. As the case may be, trees of SCGs may have labelle... |

1 |
CoGITo v3.3 : module SGBD de graphes conceptuels
- Guinaldo
- 1996
(Show Context)
Citation Context ...al subsumption relation on simple CGs. All NCG models considered in this paper generalize this simple CG model, while preserving its properties. The simple CG model has been implemented on CoGITo [4] =-=[5]-=-, a software platform for developing knowledge-based applications for which every piece of knowledge is represented by CGs. But in several applications this model proved to be inconvenient for express... |

1 |
Modelling Stereotyped Behaviours in Human Organizations
- Bos, Botella
- 1996
(Show Context)
Citation Context ...dge involved. Let us give two examples of applications we are currently involved in. First, a simulation application of the required behavior of human agents in case of a catastrophe in a factory [6] =-=[7]-=-. This behavior is described by CGs which represent situations, pre-conditions and postconditions of actions to be performed, each of these elements being themselves described by CGs. Second, a study ... |

1 |
Une utilisation des graphes conceptuels pour la recherche documentaire
- Genest
- 1996
(Show Context)
Citation Context ...sent situations, pre-conditions and postconditions of actions to be performed, each of these elements being themselves described by CGs. Second, a study of document retrieval for university libraries =-=[8]-=-. 1 & is commutative The content of a document is partially represented by a CG. At first level, the title, the author and the subject are encoded. At second and deeper levels, the subject is describe... |

1 | Conceptual Graph Language - Ghosh - 1996 |

1 |
Quelques classes de graphes embots quivalentes
- Chein, Mugnier
- 1996
(Show Context)
Citation Context ...used for building an algorithm which computes a morphism (rooted or not) between two trees of graphs, whose complexity is polynomially related to the complexity of morphism computation on the class C =-=[13]-=-. 2.3. Generalization Relation Let us first recall that a category, say C, is a class of objects, called C-objects, together with a class of morphisms, called C-morphisms, which are related in the fol... |

1 |
Une smantique logique pour les graphes embots
- Simonet
- 1996
(Show Context)
Citation Context ... with respect to this calculus, i.e. there exists a projection from a NCG G to a NCG H if and only if the sequent leading from the formula associated to G to the formula associated to H is derivable. =-=[20]-=- defines a semantics in first-order logic. And projection (from G to H) is proven to be sound and complete with respect to implication (when H has a normal form). Equivalence of NCG classes allows tra... |